Math 206 (Multivariable Differential and Integral Calculus)
The course is divided into three parts, namely:
- Differential calculus of functions of several variables.
- Integral calculus of functions of several variables.
- Sequences, numerical series and power series.
More precisely, the main contents of the course are described as follows: Functions of several variables, Domains, Limits, and Continuity. Graph of a function of two variables and Level curves. Partial derivatives, Chain rules. Differentiability of a function of two and three variables. Directional Derivatives, Equations of the tangent planes and application to linear approximation. Extrema of functions of several variables (local and absolute), Lagrange multipliers. Double integrals and applications to areas and volumes. Double integral in polar coordinates. Triple integrals, Triple integrals in cylindrical and spherical coordinates, applications to volumes. Sequences, infinite series. Positive term series Convergence tests (Integral, Comparison, Limit comparison, Ratio and Root). Alternating series, Absolute and Conditional Convergence. Power series, Radius and interval of convergence, Power series representations of functions. Maclaurin and Taylor and binomial series.